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Using a CAS/DGS to Analyze Computationally the Configuration of Planar Bar Linkage Mechanisms Based on Partial Latin Squares

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Abstract

Currently, the study of new isotopism invariants of partial Latin squares constitutes an open and active problem. This paper delves into this topic by analyzing computationally the configuration of planar bar linkage mechanisms for which the array formed by the lengths of their bars constitutes an empty-diagonal symmetric partial Latin square such that each one of its rows and columns has at least two non-empty cells. These assumptions enable one to define a series of algebraic and geometric constraints that can be readily implemented in any Computer Algebra or Dynamic Geometry System. In order to illustrate the different concepts and results introduced throughout the paper, it is explicitly determined and characterized the distribution of planar bar linkage mechanisms based on partial Latin squares of order up to five.

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  1. Department of Applied Mathematics I., University of Seville, Avenida Reina Mercedes s/n, 41012, Sevilla, Spain

    Raúl M. Falcón

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  1. Raúl M. Falcón
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Correspondence to Raúl M. Falcón.

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This work is partially supported by the Research Project FQM-016 from Junta de Andalucía, and by the Departmental Research Budget of the Department of Applied Mathematics I of the University of Seville.

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Falcón, R.M. Using a CAS/DGS to Analyze Computationally the Configuration of Planar Bar Linkage Mechanisms Based on Partial Latin Squares. Math.Comput.Sci. 14, 375–389 (2020). https://doi.org/10.1007/s11786-019-00428-1

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  • DOI: https://doi.org/10.1007/s11786-019-00428-1

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